Find the inverse relation of f(x)=(5x−2)/8

Question

algebraically by letting y=x
.(1 point)
Responses

y=(5x+2)8
y equals Start Fraction left parenthesis 5 x plus 2 right parenthesis over 8 End Fraction

y=(8x−2)5
y equals Start Fraction left parenthesis 8 x minus 2 right parenthesis over 5 End Fraction

y=85(x+2)
y equals Start Fraction 8 over 5 End Fraction left parenthesis x plus 2 right parenthesis

y=15(8x+2)

Answer 1

To find the inverse relation of the function \( f(x) = \frac{5x - 2}{8} \) algebraically, we follow these steps:

1. Let \( y = f(x) \): \[ y = \frac{5x - 2}{8} \]

2. Solve for \( x \) in terms of \( y \): \[ 8y = 5x - 2 \] \[ 5x = 8y + 2 \] \[ x = \frac{8y + 2}{5} \]

3. Now we swap \( x \) and \( y \) to find the inverse: \[ y = \frac{8x + 2}{5} \]

Thus, the inverse relation of \( f(x) \) is: \[ y = \frac{8x + 2}{5} \]

Therefore, the correct response is: \[ y = \frac{8x + 2}{5} \]